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~i40-E \ 15tHf07Con. 3358-07.

\ Gl~ \ B f ~ c. Re V ( 1 f\ 0{ ,J r 0 < ( Pr< r .. J I(REVISED COURSE)

(3 Hours) [TotalN.S. Am;wer any five questions.

State and explain with example :-(i) Conditional probability(ii) 8ayt s Theorem.If two events A and 8 are independant, show that -

, (i) A and [are independant(ii) A and Bare independant. .For a cmtaihbinarycommunicationchannel,the probabilitythat a transmitted 0 is receivedis 0.95 while the probabiiity that a transmitted 1 is received as 1 is 0.90. If the probatransmitting a 0 is 0.4, find the probability that -(i) a 1 is received(ii) a 1 was transmitted given that 1 was received(iii) the error has occured. .Define probability distribution function of random variable. State important prope:rties of it anafiy one property.I: X is poisson distributed random variable, find moment generating iunction (M.G. F.) and charaft-nction.

1. (a)

(b)

(c)

2. (a)(b)

s i dcom

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